可靠的毫米波正交干涉仪（70GHz）（二）

Many interferometers are required to operate in high ambient magnetic fields (B-fields), e.g. around magnetic confinement plasma devices. Typically, microwave sources require the use of a series isolator to prevent reflected power from returning to the oscillator causing frequency shifts. Commercially available isolators are ferromagnetic devices which must be shielded from background B-fields in order to function correctly and not be damaged. Since magnetic shielding is of general interest, the design and construction of the shielding for the isolator of this system is also described in this paper.

2. INTERFEROMETER CIRCUI

The interferometer circuit is shown in Fig. 1, above. The isolated Gunn oscillator output is divided by a 10 dB directional coupler with most power (90%) going to the LO input of the quadrature mixer, and the remainder directed into the plasma. The mixer is placed as physically close to the oscillator as possible in order to provide sufficient LO power, PLO. For example, the mixer used in this circuit, an Epslion-Lambda Electronics model ELMIX72, requires PLO greater than or equal to 15 dBm, while the Gunn oscillator (Epsilon-Lambda model ELV173) has an output power of only 17.8 dBm. Such high LO power requirements are typical of millimeter-wave quadrature mixers. The remaining source power launched into the plasma easily provides enough RF power to the mixer to give a signal to noise ratio greater than 103 for typical lab plasma parameters, as will be shown in the next section.

In order to better collimate the microwave beam, lower band (Q-band, 33-50 GHz) horns and lenses have been used. The horns are standard high gain horns, G = 20 dB. The lenses are spherical, high density polyethylene (HDPE), and are easily and inexpensively made [5]. Phase quadrature IF outputs are generated by the quadrature mixer. Quadrature mixers in millimeter-wave ranges tend to be quite narrow band. For example, the ELMIX72 has a ± 200 MHz bandwidth, centered at 70.0 GHz. To accommodate the narrow band of the mixer the oscillator must either be matched to the mixer, or have enough tuning range, while maintaining sufficient phase stability, to tune to the mixer band. In this case, the oscillator and mixer were purchased as a matched pair.

The outputs of the quadrature mixer are VIF1 = A1cos(theta) + VOFF1, VIF2 = A2sin(theta + (theta)0) + VOFF2. VOFF1 and VOFF2 are DC offsets and (theta)0 is the quadrature phase error. These may be viewed on an oscilloscope or digitized directly. Ideally, A1 = A2, VOFF1 = VOFF2 = 0, and (theta)0 = 0, so that the outputs are exactly balanced with zero offset, and exactly in quadrature. In this case the expression for theta reduces to (1). In practice there is some amplitude imbalance, offset, and quadrature error which are functions of frequency and LO power, so that the ideal conditions stated above are not met. However, for a given frequency and LO power, the system can be calibrated by determining A1, A2, VOFF1, VOFF2 and (theta)0, so that theta remains the only unknown. The phase shift as a function of time, theta(t), can easily be computed from

 (2)

Calibration to determine A1, A2, VOFF1, VOFF2 and (theta)0 is accomplished by adding a variable phase shifter to the reference leg and sweeping through a 2 pi phase shift with no plasma present. Alternately, the receiving horn and mixer can be mounted on a moveable base, provided there is enough flexibility in the reference waveguide (in this case less than 5 mm). When the receiving horn is moved toward the launch horn to sweep through a 2 pi phase shift (with no plasma), the IF outputs trace out sinusoidal voltages with amplitudes A1, and A2, DC offsets VOFF1, and VOFF2 , and have an error (theta)0 in phase quadrature. These can be measured to obtain calibration values.

The phase shift is related to the electron density by

where ne(x,t) is the electron density, e and me are the electron charge and mass respectively, e0 is the permittivity of free space, and a slab plasma is assumed. The normalized density profile, alpha*ne(x), can be measured by a scanned Langmuir probe so that eq. (3) may be integrated numerically. Alternately, the chord-averaged density can be computed eliminating the integral.

Magnetic shielding is essential if the ambient field at the microwave isolator exceeds 20 Gauss, since it contains a magnet. The source must be kept close to the vacuum window, and therefore in the background B-field, in order to avoid excessive power loss. The shield used here consists of two concentric iron pipes and a layer of mu-metal, as shown in the assembly drawing, Fig. 2.

The iron has a fairly low magnetic constant, mu = 100, but is not easily saturated. The opposite is true for the mu-metal (mu > 10,000). To prevent saturation it is placed on the innermost wall of the pipe. Such multiple shells have been shown to be highly effective as shields [6]. For example, three concentric shields each with mu = 100 are as effective as a single one with mu = 1000. The axis of the shield is parallel to the stray magnetic field from the plasma device. In our application the field at the isolator is reduced from 200 Gauss to 2 Gauss. Care must be taken to secure the iron shields lest they twist when the B-field is turned on.